Perpendicular Line Calculator
Perpendicular Line Calculator is an online tool that calculates and displays the equation of a perpendicular line.
What is a Perpendicular Line Calculator?
Perpendicular Line Calculator helps you to easily find the equation of a perpendicular line within a few seconds.
Perpendicular Line Calculator
NOTE: Enter numbers up to 2 digits only.
How to Use the Perpendicular Line Calculator?
Follow the steps given below to use the calculator:
- Step 1 : Enter the values for the equation of the line and the coordinates in the respective input boxes.
- Step 2 : Click on "Calculate" to get the equation of the perpendicular line.
- Step 3 : Click on "Reset" to clear the fields and enter the new values.
What is Meant by Equation of a Perpendicular Line?
When two lines intersect at right angles (90°), we call them perpendicular lines. To find the equation of a line which is perpendicular to another line:
- Write the given equation of the line in terms of ' y = mx + b '. Here 'y' is the line, 'x' is the slope of the line and 'b' is the point where the line intercepts the y-axis.
- In order to find the slope of the line which is perpendicular to the given line, first, take the negative reciprocal of the given line 'y = mx + b', which will be '-1/m'.
- Then, find the value of 'b' by substituting the coordinate points (x,y) through which the perpendicular line passes.
- Finally, form the equation of the perpendicular line by substituting the values of '(-1/m) and 'b'.
Let us understand this with the following example.
Solved Examples on Perpendicular Line Calculator
Example 1:
Find the equation of the line that is perpendicular to the line 3y - x = 6, passing through the points (4,2).
Solution:
Step 1:
Rewrite the given equation in the form of 'y = mx + b'.
3y - x = 6
3y = 6 + x
y = (6/3) + (x/3)
y = 2 + (x/3) or y = ((1/3) × x) + 2
Therefore, slope (m) = 1/3
Step 2 :
Find the negative reciprocal of the slope.
Slope = 1/3; Negative reciprocal of slope (m) = -3
Step 3:
The perpendicular line passes through the coordinates (4,2) with slope value equal to -3.
Therefore, the equation becomes: 2 = ((-3) × 4) + b
After solving the equation, we get b = 14
Step 4 :
The equation of the perpendicular line is: y = ((-3) × x) + 14
y = -3x + 14
Now, try the perpendicular line calculator to find the perpendicular line equation of the following lines.
Example 2:
Find the equation of the line that is perpendicular to the line 5x - y = -12, passing through the points (3, 7).
Solution:
Step 1:
Rewrite the given equation in the form of 'y = mx + b'.
5x - y = -12
y - 5x = 12
y = 5x + 12
Therefore, slope (m) = 5
Step 2 :
Find the negative reciprocal of the slope.
Slope = 5; Negative reciprocal of slope (m) = -1/5
Step 3:
The perpendicular line passes through the coordinates (3, 7) with slope value equal to -1/5.
Therefore, the equation becomes: 7 = ((-1/5) × 3) + b
After solving the equation, we get b = 38/5
Step 4 :
The equation of the perpendicular line is: y = ((-1/5) × x) + 38/5
y = (-1/5)x + 38/5
Now, try the perpendicular line calculator to find the perpendicular line equation of the following lines.
- 5x + 6y = 10, passing through the coordinates (2,3).
- 2x + y = 4, passing through the coordinates (1,2).